# How to do error correction after encoded Bell measurement?

Need some help with the concepts of encoded/logical bell measurement.

Please visualize the picture in your mind. Suppose I have a node with 7+7 qubits side by side, left 7 is $$|0_{L}\rangle$$ and right 7 is $$|+_{L}\rangle$$. Suppose $$|0_{L}\rangle$$ = $$|1001011\rangle$$ and $$|+_{L}\rangle$$ = $$|0011011\rangle$$. Now I apply $$CNOT$$ between each pair of left and right qubits and after that $$H$$ gate on the all left side 7 qubits.

Now the problem how do I error correction. This part I am having confusion. I have an idea but I am having doubt.

Do I need to take additional 7 qubits for the left side and apply $$CZ$$ on each one and similarly additional 7 qubits for the right side and apply $$CX$$? This idea came after seeing the bell measurement from teleportation. This part is bothering, since those are logical qubits.

• How come $|+_L\rangle$ is orthogonal to $|0_L\rangle$? They should have an inner product of $1/\sqrt2$. Also, how do these states relate to whatever error correcting code you're wanting to use? Jul 7, 2021 at 6:43 